Correlation Functions of Multisite Interaction Spin-S models on the Bethe-like Lattices

TL;DR

This paper develops an exact recursive method to compute correlation functions, correlation length, and magnetic susceptibility for multisite interaction spin-S models on Bethe-like lattices, revealing critical behavior and phase transition properties.

Contribution

It extends the transfer-matrix method to exactly calculate correlation functions and critical parameters for multisite interaction spin models on Bethe-like lattices, providing new analytical insights.

Findings

Correlation length diverges with critical index ν=1.

Magnetic susceptibility is proportional to correlation length in second order phase transitions.

Exact expressions for correlation length and susceptibility are derived for spin-1/2 models.

Abstract

Multisite interaction spin-S models in an external magnetic field are studied recursively on the Bethe-like lattices. The transfer-matrix method is extended to calculate exactly the two-spin correlation functions. The exact expressions for the correlation length and magnetic susceptibility are derived for spin-1/2 models. The singularity of the correlation length with critical index $\nu =1$ and the proportionality of magnetic susceptibility to correlation length in the second order phase transition region of spin-1/2 ferromagnetic models on the Bethe-like lattices are established analytically.